Lecture

Support Vector Machines: Kernel Tricks

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

EE-311: Fundamentals of machine learning

Ce cours présente une vue générale des techniques d'apprentissage automatique, passant en revue les algorithmes, le formalisme théorique et les protocoles expérimentaux. ...

Description

This lecture covers the concept of kernel tricks in support vector machines, allowing for efficient computation in high-dimensional spaces without explicit transformation. It explains the definition of kernels, the Moore-Aronszajn theorem, and various types of kernels such as quadratic, polynomial, and Gaussian radial. The lecture also discusses the application of kernels in SVMs, the Gram matrix, and the use of redescription spaces for non-linear decision functions.

Instructors (2)

Michael Stefan Daniel Liebling

Teaching & PhD Past EPFL PhD Students as codirector Christian Jaques, Olivia Mariani, Adrian Shajkofci, François Thierry M Marelli Courses Fundamentals of machine learning EE-311 This course provides a general overview of machine learning, covering the main algorithms, theoretical formalisms, and experimental protocols.

François Fleuret

Official source

Related concepts (29)

Radial basis function kernel

In machine learning, the radial basis function kernel, or RBF kernel, is a popular kernel function used in various kernelized learning algorithms. In particular, it is commonly used in support vector machine classification. The RBF kernel on two samples and x', represented as feature vectors in some input space, is defined as may be recognized as the squared Euclidean distance between the two feature vectors. is a free parameter.

Polynomial kernel

In machine learning, the polynomial kernel is a kernel function commonly used with support vector machines (SVMs) and other kernelized models, that represents the similarity of vectors (training samples) in a feature space over polynomials of the original variables, allowing learning of non-linear models. Intuitively, the polynomial kernel looks not only at the given features of input samples to determine their similarity, but also combinations of these. In the context of regression analysis, such combinations are known as interaction features.

Invertible matrix

In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or (rarely used) regular), if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.

Definite matrix

In mathematics, a symmetric matrix with real entries is positive-definite if the real number is positive for every nonzero real column vector where is the transpose of . More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real number is positive for every nonzero complex column vector where denotes the conjugate transpose of Positive semi-definite matrices are defined similarly, except that the scalars and are required to be positive or zero (that is, nonnegative).

Quadratic form

In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, is a quadratic form in the variables x and y. The coefficients usually belong to a fixed field K, such as the real or complex numbers, and one speaks of a quadratic form over K. If , and the quadratic form equals zero only when all variables are simultaneously zero, then it is a definite quadratic form; otherwise it is an isotropic quadratic form.

Related lectures (64)

Mercer Theorem and Kernels

Explores the Mercer Theorem, Kernels, and their role in machine learning applications.

Support Vector Machines: Kernel SVM

Explores non-linear SVM using kernels for data separation in higher-dimensional spaces, optimizing training with kernels to avoid explicit transformations.

Feature Expansion: Kernels and KNN

Covers feature expansion, kernels, and K-nearest neighbors, including non-linearity, SVM, and Gaussian kernels.

Feature Expansion and Kernels

Covers feature expansion, kernels, SVM, and nonlinear classification in machine learning.

Kernel Methods: Machine Learning